Prof. Charles M. Newman, gave a lecture titled“Riemann Hypothesis and Mathematical Physics”at AMSS on 21, December 2017.

In both analytic number theory (the Riemann Hypothesis) and mathematical physics (Ising models and Euclidean field theories) the following complex analysis issue arises. For $\rho$ a finite positive measure on the real line $\mathbb{R}$, let $H(z; \rho, \lambda)$ denote the Fourier transform of $\exp\{\lambda u^2\} d\rho (u)$, i.e., the integral over $\mathbb{R}$ of $\exp\{izu + \lambda u^2\} d\rho (u)$ extended from real to complex $z$, for those $\lambda$ (including all $\lambda < 0$) where this is possible. The issue is to determine for various $\rho$'s those $\lambda$'s for which all zeros of $H$ in the complex plane are real. They would discuss some old and new theorems about this issue.

Prof. Charles M. Newman, Silver Professor of Mathematics at the Courant Institute and Global Network Professor at NYU-New York and NYU-Shanghai, received B.S. degrees in Mathematics and in Physics from MIT and M.S. and Ph.D. degrees in Physics from Princeton. With 200+ published papers, mainly in probability and statistical physics, he has been a Sloan and Guggenheim fellow and is a member of the U.S. National Academy of Sciences, the American Academy of Arts and Sciences and the Brazilian Academy of Sciences.